February 1 Math Colloquium

Jared Corduan, Input Output HK

The Amazingly Useful Pigeon Hole Principle

Both the finite and the infinite pigeon hole principle are extremely simple facts that have surprisingly useful consequences. The principle is closely related to mathematical induction and is the entryway to Ramsey theory. Though simple, the infinite version fails to be constructive. In particular, it is not valid from the point of view of intuitionism. In 1990, however, Bezem and Veldman found a statement which is classically equivalent to the infinite pigeon hole principle, preserves its meaning, and has a constructive proof. Proof assistants such as LEAN are an insightful way to examine such proofs.